Rewrite the logarithmic expression $\log(A\sqrt{B})+\log(A^2)$ in equivalent logarithmic form. There may be more than one correct answer.

A. $\log(A) - 2\log(B) + \log(A^2)$

B. $\log(A^3\sqrt{B})$

C. $3\log(A)+\frac{1}{2}\log(B)$

D. $\log(A^{3}) + \frac{1}{2}\log(B)$

E. $\log(A) + \frac{1}{2}\log(B) + \log(A^2)$

F. $\frac{\log(A)\log(B)}{2} + 2\log(A)$

G. None of the above